Question

Mojave art club is selling t shirts for a fundraiser. A local company charges $35 to set up the logo and $4.25 per t shirt if x t shirts are printed by the business.

If the art club charged $10 per shirt how many shirts would need to be sold to cover their costs?

function C(x)=35+4.25x/x

Answer 1

At least 7 shirts would need to be sold to cover their costs

Explanation:

Cost of producing x t-shirts.

The cost of producing x t-shirts is a flat fee of 35 plus 4.25 per t-shirt. So

`C(x) = 35 + 4.25x`

Earnings of selling x t-shirts:

Charges $10 per t-shirt, so it earns 10 for each t-shirt it sells.

`E(x) = 10x`

How many shirts would need to be sold to cover their costs?

To cover the costs, we need that the earnings are equal or higher than the costs. So

`E(x) \geq C(x)`

`10x \geq 35 + 4.25x`

`5.75x \geq 35`

`x \geq (35)/(5.75)`

`x \geq 6.09`

Since we cannot sell a decimal part of a shirt, at least 7 shirts would need to be sold to cover their costs